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A208188 Number of distinct n-colored necklaces with 7 beads per color. 2
1, 1, 246, 19003476, 16875655269948, 90784545100668913392, 2041012695880532470281654960, 150277870737901828652705825755721760, 30495546426686489361833408314854897254404320, 14997592385781765578538605874290442908069285068834560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..35

FORMULA

a(n) = Sum_{d|7} phi(7/d)*(n*d)!/(d!^n*n*7) if n>0 and a(0) = 1.

EXAMPLE

a(0) =   1: the empty necklace.

a(1) =   1: {0000000}.

a(2) = 246: {00000001111111, ..., 01010101010101}.

MAPLE

with(numtheory);

a:= n-> `if`(n=0, 1, add(phi(7/d) *(n*d)!/(d!^n *7*n), d={1, 7})):

seq(a(n), n=0..12);

CROSSREFS

Row n=7 of A208183.

Cf. A000010, A000142.

Sequence in context: A229478 A289334 A251516 * A177212 A044983 A175043

Adjacent sequences:  A208185 A208186 A208187 * A208189 A208190 A208191

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 24 2012

STATUS

approved

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Last modified March 25 01:17 EDT 2019. Contains 321450 sequences. (Running on oeis4.)